# nLab B1-homotopy theory

Contents

### Context

#### Analytic geometry

analytic geometry (complex, rigid, global)

## Basic concepts

analytic function

analytification

GAGA

# Contents

## Idea

$\mathbb{B}^1$-homotopy theory is the study of the localization of an (∞,1)-sheaf (∞,1)-category over a site of analytic spaces at morphisms $\mathbb{B}^1 \to *$, where $\mathbb{B}^1 \simeq Spm(k\{t\})$ is the Tate ball.

## References

• Joseph Ayoub, Motives of rigid varieties and

the motivic nearby functor_, talk notes 2006 (pdf)

• Joseph Ayoub, Motifs des variétés analytiques rigides (pdf)

• Joseph Ayoub, Floian Ivorra and Julien Sebag, Motives of rigid analytic tubes and nearby motivic sheaves (pdf)

Last revised on June 11, 2014 at 07:12:11. See the history of this page for a list of all contributions to it.